Coupled transport in rotor models

S. Iubini; S. Lepri; R. Livi; A. Politi

doi:10.1088/1367-2630/18/8/083023

Coupled transport in rotor models

S. Iubini, S. Lepri, R. Livi, A. Politi

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Abstract

Steady nonequilibrium states are investigated in a one-dimensional setup in the presence of two thermodynamic currents. Two paradigmatic nonlinear oscillators models are investigated: an XYchain and the discrete nonlinear Schrödinger equation. Their distinctive feature is that the relevant variable is an angle in both cases. We point out the importance of clearly distinguishing between energy and heat flux. In fact, even in the presence of a vanishing Seebeck coefficient, a coupling between (angular) momentum and energy arises, mediated by the unavoidable presence of a coherent energy flux. Such a contribution is the result of the ‘advection’ induced by the position-dependent angular velocity. As a result, in the XY model, the knowledge of the two diagonal elements of the
Onsager matrix suffices to reconstruct its transport properties. The analysis of the nonequilibrium steady states finally allows to strengthen the connection between the two models.

Original language	English
Article number	083023
Pages (from-to)	1-11
Number of pages	11
Journal	New Journal of Physics
Volume	18
DOIs	https://doi.org/10.1088/1367-2630/18/8/083023
Publication status	Published - 3 Aug 2016

Bibliographical note

Acknowledgement
One of us (AP) wishes to acknowledge S. Flach for enlightening discussions about the relationship between the DNLS equation and the rotor model.

Keywords

transport processes
heat transfer (theory)
nonlinear oscillators
XY model
discrete nonlinear Schrdinger equation

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10.1088/1367-2630/18/8/083023Licence: CC BY

Coupled transport in rotor models
Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. https://creativecommons.org/licenses/by/3.0/
Final published version, 1.24 MBLicence: CC BY

Cite this

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title = "Coupled transport in rotor models",

abstract = "Steady nonequilibrium states are investigated in a one-dimensional setup in the presence of two thermodynamic currents. Two paradigmatic nonlinear oscillators models are investigated: an XYchain and the discrete nonlinear Schr{\"o}dinger equation. Their distinctive feature is that the relevant variable is an angle in both cases. We point out the importance of clearly distinguishing between energy and heat flux. In fact, even in the presence of a vanishing Seebeck coefficient, a coupling between (angular) momentum and energy arises, mediated by the unavoidable presence of a coherent energy flux. Such a contribution is the result of the {\textquoteleft}advection{\textquoteright} induced by the position-dependent angular velocity. As a result, in the XY model, the knowledge of the two diagonal elements of theOnsager matrix suffices to reconstruct its transport properties. The analysis of the nonequilibrium steady states finally allows to strengthen the connection between the two models.",

keywords = "transport processes, heat transfer (theory), nonlinear oscillators, XY model, discrete nonlinear Schrdinger equation",

author = "S. Iubini and S. Lepri and R. Livi and A. Politi",

note = "Acknowledgement One of us (AP) wishes to acknowledge S. Flach for enlightening discussions about the relationship between the DNLS equation and the rotor model.",

year = "2016",

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day = "3",

doi = "10.1088/1367-2630/18/8/083023",

language = "English",

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TY - JOUR

T1 - Coupled transport in rotor models

AU - Iubini, S.

AU - Lepri, S.

AU - Livi, R.

AU - Politi, A.

N1 - Acknowledgement One of us (AP) wishes to acknowledge S. Flach for enlightening discussions about the relationship between the DNLS equation and the rotor model.

PY - 2016/8/3

Y1 - 2016/8/3

N2 - Steady nonequilibrium states are investigated in a one-dimensional setup in the presence of two thermodynamic currents. Two paradigmatic nonlinear oscillators models are investigated: an XYchain and the discrete nonlinear Schrödinger equation. Their distinctive feature is that the relevant variable is an angle in both cases. We point out the importance of clearly distinguishing between energy and heat flux. In fact, even in the presence of a vanishing Seebeck coefficient, a coupling between (angular) momentum and energy arises, mediated by the unavoidable presence of a coherent energy flux. Such a contribution is the result of the ‘advection’ induced by the position-dependent angular velocity. As a result, in the XY model, the knowledge of the two diagonal elements of theOnsager matrix suffices to reconstruct its transport properties. The analysis of the nonequilibrium steady states finally allows to strengthen the connection between the two models.

AB - Steady nonequilibrium states are investigated in a one-dimensional setup in the presence of two thermodynamic currents. Two paradigmatic nonlinear oscillators models are investigated: an XYchain and the discrete nonlinear Schrödinger equation. Their distinctive feature is that the relevant variable is an angle in both cases. We point out the importance of clearly distinguishing between energy and heat flux. In fact, even in the presence of a vanishing Seebeck coefficient, a coupling between (angular) momentum and energy arises, mediated by the unavoidable presence of a coherent energy flux. Such a contribution is the result of the ‘advection’ induced by the position-dependent angular velocity. As a result, in the XY model, the knowledge of the two diagonal elements of theOnsager matrix suffices to reconstruct its transport properties. The analysis of the nonequilibrium steady states finally allows to strengthen the connection between the two models.

KW - transport processes

KW - heat transfer (theory)

KW - nonlinear oscillators

KW - XY model

KW - discrete nonlinear Schrdinger equation

U2 - 10.1088/1367-2630/18/8/083023

DO - 10.1088/1367-2630/18/8/083023

M3 - Article

SN - 1367-2630

VL - 18

SP - 1

EP - 11

JO - New Journal of Physics

JF - New Journal of Physics

M1 - 083023

ER -

Coupled transport in rotor models

Abstract

Bibliographical note

Keywords

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